潘维民 何 骏. 基于密度聚类的神经模糊系统建模算法[J]. 计算机研究与发展, 2010, 47(11): 1986-1992.
 引用本文: 潘维民 何 骏. 基于密度聚类的神经模糊系统建模算法[J]. 计算机研究与发展, 2010, 47(11): 1986-1992.
Pan Weimin and He Jun. Neuro-Fuzzy System Modeling with Density-Based Clustering[J]. Journal of Computer Research and Development, 2010, 47(11): 1986-1992.
 Citation: Pan Weimin and He Jun. Neuro-Fuzzy System Modeling with Density-Based Clustering[J]. Journal of Computer Research and Development, 2010, 47(11): 1986-1992.

## Neuro-Fuzzy System Modeling with Density-Based Clustering

• 摘要: 神经模糊系统经常被用来对非线性系统建模，并能取得很好的效果.以往的模糊系统建模方法存在着输入空间划分个数难以确定和规则冗余的问题，这些问题阻碍了模糊系统的应用.基于动态阈值DENCLUE和相似规则合并的神经模糊系统建模算法DDTSRM(DENCLUE using a dynamic threshold and similar rules merging)，首先在DENCLUE算法中使用动态阈值来合并密度吸引子，得到DDT算法.DDTSRM利用DDT算法不依赖初始参数的特点，解决了输入空间划分个数难以确定的问题.因为DDT算法可以得到任意形状和任意密度的聚类结果的特性，所以提高了模糊系统模型的准确性.辨识出模型的初始结构后，DDTSRM通过计算模糊集合之间的相似度来减少规则冗余，使模糊系统模型结构得到优化.最后利用BP算法对系统模型进行训练，进而提高系统的建模精度.以S-Y模糊系统模型为原型，在两输入一输出的非线性函数和Box-Jenkins数据上的仿真实验证明了DDTSRM算法在神经模糊系统建模应用的有效性，能够取得精确的建模效果.

Abstract: Neuro-fuzzy system is widely used for nonlinear system modeling. How to partition the input space optimally is the core issue in fuzzy system modeling. Previous ways suffer from two main drawbacks, the difficulty to determine of the number of partitions and rule redundancy, which hinders the application of fuzzy system. The authors present a new approach to neuro-fuzzy system modeling based on DENCLUE using a dynamic threshold and similar rules merging (DDTSRM). They first introduce DDT, which uses a dynamic threshold rather than a global threshold in merging density-attractors in DENCLUE. DDTSRM is good at determining the number of rules because DDT does not depend on input parameters. Additionally, the modeling performance is improved for DDT can find arbitrary shape and arbitrary density clusters. Rule redundancy is caused by similar fuzzy sets in the input and output data space. After structure identification, similar rules are merged by considering similarity measures between fuzzy sets. This is also effective for the model to avoid overfitting to the sample data. Finally, BP method is used to precisely adjust the parameters of the fuzzy model. DDTSRM is applied to a nonlinear function and Box and Jenkins system. Experimental results show that DDTSRM has overcome the drawbacks with a good performance.

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